TY - JOUR
T1 - Default functions and Liouville type theorems based on symmetric diffusions
AU - Atsuji, Atsushi
N1 - Funding Information:
2010 Mathematics Subject Classification. Primary 31C05; Secondary 58J65. Key Words and Phrases. Brownian motion on manifolds, strictly local submartingale, subharmonic function, L1-Liouville theorem, Liouville theorem for holomorphic maps. Partially supported by the Grant-in-Aid for Scientific Research 17K18741, Japan Society for the Promotion of Science.
Publisher Copyright:
© 2021 The Mathematical Society of Japan
PY - 2021/4
Y1 - 2021/4
N2 - Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps.
AB - Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps.
KW - Brownian motion on manifolds
KW - L-Liouville theorem
KW - Liouville theorem for holomorphic maps
KW - Strictly local submartingale
KW - Subharmonic function
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U2 - 10.2969/JMSJ/82398239
DO - 10.2969/JMSJ/82398239
M3 - Article
AN - SCOPUS:85105949949
SN - 0025-5645
VL - 73
SP - 525
EP - 551
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
IS - 2
ER -